Background

This document has nls (non-linear least squares) regression fits using the log-normal functional form to USFS FIA (United States Forest Service Forest Inventory & Analysis) biomass growth vs. stand age relationships. This functional form is commonly used in growth analyses, and permits a flexible shape to fit to data in an intermediate maximum (i.e., “hump” shaped) relationship. We use the sum of tree biomass growth increment method for the plot biomass growth (\(G\)) calculation (see supplementary methods). Models are fitted separately by US ecoprovince.

Hypothetically, the entire functional form of the following non-linear model is considered: \(G = (1 + (yr-1990) \cdot ge/100) \times (1 - \alpha \cdot B_l) \times (1 + \phi \cdot \Delta PDSI) \times \left(a + b \cdot \exp{ - \left[ \frac{ \log \left( StdAge_{t1} /c \right)} {d} \right]} ^2 \right)\), where \(G\) is the plot level biomass growth calculated as the sum of tree biomass growth increments, \(B_l\) is the calculated proportion of biomass loss over the census interval, \(StdAge_{t1}\) is the FIA-estimated stand age at the first of two FIA plot tree censuses, \(\Delta PDSI\) is the difference in the growing season (January-August) annual average PDSI values over the FIA plot measurement intervals and a 30-year climate normal (1969-1990), and \(yr\) is the measurement year (all FIA data). Free parameters are \(\alpha\): the growth compensation of lost plot biomass, \(ge\): biomass growth enhancement over time, \(a\): the y-intercept of the curve, \(a +b\): the peak value of \(G\), \(c\): the \(StdAge_{t1}\) value at peak \(G\), and \(d\): the curve shape parameter.

Data have increasing variance in \(G\) with increasing \(StdAge_{t1}\), Thus, weighted nls is the best approach. We explore a few weighting options and found that proportional weighting can be achieved by weighting observations by \(\frac {1} {meanG}\) in equal-sample sized plot biomass bins (n=20) for each ecoprovince.

Model selection is used to determine. to determine the best fitting models, which is implemented in two parts. A first model selection is done to determine the best model form either including \(\alpha\): the biomass compensation effect due to lost biomass (natural mortality or harvest), \(\phi\): the effect of changing climate (quantified as \(\Delta PDSI\), or both. \(\Delta PDSI\) is defined the difference in the Palmer drought severity index from January - August for the 10 years preceding the biomass measurement and the 1969-1990 period). We explored \(\Delta PDSI\) using only the summer growing months (June-August) over the same intervals, and analyses were insensitive to that change. For the first model selection the following models are considered:

model 1: simple model \(G = (1 + (yr-1990) \cdot ge/100) \times \left(a + b \cdot \exp{ - \left[ \frac{ \log \left( StdAge_{t1} /c \right)} {d} \right]} ^2 \right)\)

model 2: phi model \(G = (1 + (yr-1990) \cdot ge/100) \times (1 + \phi \cdot \Delta PDSI) \times \left(a + b \cdot \exp{ - \left[ \frac{ \log \left( StdAge_{t1} /c \right)} {d} \right]} ^2 \right)\)

model 3: phi-alpha model \(G = (1 + (yr-1990) \cdot ge/100) \times (1 + \phi \cdot \Delta PDSI) \times (1 - \alpha \cdot B_l) \times \left(a + b \cdot \exp{ - \left[ \frac{ \log \left( StdAge_{t1} /c \right)} {d} \right]} ^2 \right)\)

NOTE:

This document contains all \(G\) observations that meet our plot based filtering criteria:

exclude FIA plots in plantation forests
exclude FIA plots with multiple plot conditions (COND_PROG_UNADJ > 0.95)
exclude FIA plots non-productive stands (i.e., those with less than 20 ft^3/acre/year timber producing capability; SITECLCD of 7)
exclude FIA plots in non-stocked stands (i.e., those with STDSZCD of 5)
exclude FIA plots in non-accessible areas (i.e., private lands etc., COND_STATUS_CD not equal to 1)
exclude FIA plot visits that are not part of the annual inventories (which also includes FIA plot visits for Phase 3 ozone measurements)

Additionally, in an effort to clean up the data set, we have removed outlier observations, using a quantile threshold approach. We also calculated plot \(G\) using as biomass balance method (see supplementary methods), and the difference between the two methods. Accordingly, we define \(diff_G\) as the difference between tree incremental \(G\) and biomass balance \(G\). We excluded observations which meet the following criteria using a 0.5% quantile (\(QT\)):

case A: where the \(QT\) difference in tree incremental \(G\) is > biomass balance plot G (i.e., > 99.5% \(diff_G\) positive outliers)
case B: where the \(QT\) difference in tree incremental \(G\) is < mass balance plot G (i.e., < 0.5% \(diff_G\) negative outliers)
case C: where the \(QT\) difference in tree incremental \(G\) is > 0 (i.e., > 99.5% positive outliers)
case D: where the \(QT\) difference in tree incremental \(G\) is > 0 (i.e., < 0.5% negative outliers)

These data set cleaning criteria resulted in the exclusion of 1677 observations.

Below the model fitting procedure is implemented by ecoprovince:

211 - Northeastern Mixed Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 2: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 3: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
##   Res.Df Res.Sum Sq Df  Sum Sq  F value  Pr(>F)    
## 1   6818     5262.8                                
## 2   6817     5259.1  1   3.714   4.8147 0.02825 *  
## 3   6816     4966.7  1 292.458 401.3532 < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 25359.00
## 2     2 25356.19
## 3     3 24967.80

## 
## Formula: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * 
##     (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * 
##     exp(-((log(STDAGE_t1/c))/d)^2))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge     0.287459   0.163111   1.762   0.0781 .  
## phi    0.010450   0.004348   2.404   0.0163 *  
## alpha  0.642950   0.030062  21.388   <2e-16 ***
## a     -6.708801  17.637541  -0.380   0.7037    
## b     10.122087  17.627165   0.574   0.5658    
## c     29.515767   1.965151  15.020   <2e-16 ***
## d      5.023528   4.707128   1.067   0.2859    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.8536 on 6816 degrees of freedom
## 
## Number of iterations to convergence: 9 
## Achieved convergence tolerance: 8.269e-06
##   (2 observations deleted due to missingness)

summary

simple model: fits
phi model: fits
phi-alpha model: fits

plot residuals

predict and plot

## Warning: Removed 233 rows containing non-finite values (stat_summary_bin).

## Warning: Removed 236 rows containing missing values (geom_point).

## Warning: Removed 1 rows containing missing values (geom_pointrange).

## Warning: Removed 62 row(s) containing missing values (geom_path).

plotting 2

212 - Laurentian Mixed Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 2: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 3: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
##   Res.Df Res.Sum Sq Df  Sum Sq  F value    Pr(>F)    
## 1  18837      17004                                  
## 2  18832      16934  5   70.65   15.713 1.805e-15 ***
## 3  18831      15835  1 1098.67 1306.545 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 67134.93
## 2     2 67048.33
## 3     3 65786.65

## 
## Formula: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * 
##     (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * 
##     exp(-((log(STDAGE_t1/c))/d)^2))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge     0.805126   0.140548   5.728 1.03e-08 ***
## phi    0.026560   0.002942   9.027  < 2e-16 ***
## alpha  0.826561   0.021000  39.361  < 2e-16 ***
## a      1.184607   0.196870   6.017 1.81e-09 ***
## b      1.437877   0.186302   7.718 1.24e-14 ***
## c     19.812728   0.783480  25.288  < 2e-16 ***
## d      1.896925   0.213805   8.872  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.917 on 18831 degrees of freedom
## 
## Number of iterations to convergence: 8 
## Achieved convergence tolerance: 8.329e-06
##   (48 observations deleted due to missingness)

summary

simple model: fits
phi model: fits
phi-alpha model: fits

plot residuals

predict and plot

## Warning: Removed 699 rows containing non-finite values (stat_summary_bin).

## Warning: Removed 750 rows containing missing values (geom_point).

## Warning: Removed 1 rows containing missing values (geom_pointrange).

## Warning: Removed 162 row(s) containing missing values (geom_path).

plotting 2

221 - Eastern Broadleaf Forest

model selection 1

## Warning in log(STDAGE_t1/c): NaNs produced

## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model

## Warning in log(STDAGE_t1/c): NaNs produced

## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
##   model      AIC
## 1     1       NA
## 2     2 31775.02
## 3     3       NA

## 
## Formula: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * 
##     (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## 
## Parameters:
##      Estimate Std. Error t value Pr(>|t|)    
## ge  -1.345701   0.094706 -14.209   <2e-16 ***
## phi  0.002627   0.004904   0.536   0.5922    
## a    4.878560   0.119267  40.905   <2e-16 ***
## b    0.761089   0.329370   2.311   0.0209 *  
## c   25.244861   1.446941  17.447   <2e-16 ***
## d   -0.144102   0.070933  -2.032   0.0422 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.113 on 7315 degrees of freedom
## 
## Number of iterations to convergence: 22 
## Achieved convergence tolerance: 5.566e-06
##   (8 observations deleted due to missingness)

summary

simple model: does not fit
phi model: fits
phi-alpha model: does not fit

plot residuals

predict and plot

## Warning: Removed 246 rows containing non-finite values (stat_summary_bin).

## Warning: Removed 248 rows containing missing values (geom_point).

## Warning: Removed 1 rows containing missing values (geom_pointrange).

## Warning: Removed 100 row(s) containing missing values (geom_path).

plotting 2

222 - Midwest Broadleaf Forest

model selection 1

## Warning in log(STDAGE_t1/c): NaNs produced

## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model

## Warning in log(STDAGE_t1/c): NaNs produced

## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model

## Warning in log(STDAGE_t1/c): NaNs produced

## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
##   model AIC
## 1     1  NA
## 2     2  NA
## 3     3  NA

## Warning in min(AIC1_222$AIC, na.rm = T): no non-missing arguments to min;
## returning Inf

## Error in h(simpleError(msg, call)) : 
##   error in evaluating the argument 'object' in selecting a method for function 'summary': object 'nls_222.' not found

summary

simple model: does not fit
phi model: does not fit
phi-alpha model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

223 - Central Interior Broadleaf Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 2: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 3: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
##   Res.Df Res.Sum Sq Df  Sum Sq F value    Pr(>F)    
## 1   8900      10536                                 
## 2   8899      10518  1  18.627  15.760 7.247e-05 ***
## 3   8895      10278  4 240.169  51.965 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 36721.56
## 2     2 36707.80
## 3     3 36494.55

## 
## Formula: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * 
##     (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * 
##     exp(-((log(STDAGE_t1/c))/d)^2))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge    -1.309507   0.094562 -13.848  < 2e-16 ***
## phi   -0.024412   0.005859  -4.167 3.12e-05 ***
## alpha  0.603657   0.040209  15.013  < 2e-16 ***
## a      2.605154   0.694499   3.751 0.000177 ***
## b      2.313894   0.681731   3.394 0.000691 ***
## c     27.311405   1.976096  13.821  < 2e-16 ***
## d      1.620595   0.379452   4.271 1.97e-05 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.075 on 8895 degrees of freedom
## 
## Number of iterations to convergence: 10 
## Achieved convergence tolerance: 3.635e-06
##   (12 observations deleted due to missingness)

summary

simple model: fits
phi model: fits
phi-alpha model: fits

plot residuals

predict and plot

## Warning: Removed 4 rows containing missing values (geom_point).

plotting 2

231 - Southeastern Mixed Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 2: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 3: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
##   Res.Df Res.Sum Sq Df Sum Sq   F value  Pr(>F)    
## 1  13361      37545                                
## 2  13360      37529  1   16.0    5.6833 0.01714 *  
## 3  13359      34363  1 3165.8 1230.7557 < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 72453.54
## 2     2 72449.86
## 3     3 71273.92

## 
## Formula: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * 
##     (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * 
##     exp(-((log(STDAGE_t1/c))/d)^2))
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## ge    -0.69766    0.09287  -7.512 6.17e-14 ***
## phi   -0.01632    0.00481  -3.393 0.000693 ***
## alpha  0.89405    0.02300  38.877  < 2e-16 ***
## a      3.90919    0.26051  15.006  < 2e-16 ***
## b      4.08267    0.24109  16.934  < 2e-16 ***
## c     18.00850    0.44007  40.922  < 2e-16 ***
## d      1.23768    0.08322  14.872  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.604 on 13359 degrees of freedom
## 
## Number of iterations to convergence: 9 
## Achieved convergence tolerance: 5.066e-06
##   (35 observations deleted due to missingness)

summary

simple model: fits
phi model: fits
phi-alpha model: fits

plot residuals

predict and plot

## Warning: Removed 455 rows containing non-finite values (stat_summary_bin).

## Warning: Removed 480 rows containing missing values (geom_point).

## Warning: Removed 1 rows containing missing values (geom_pointrange).

## Warning: Removed 79 row(s) containing missing values (geom_path).

plotting 2

232 - Outer Coastal Plain Mixed Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 2: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 3: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
##   Res.Df Res.Sum Sq Df  Sum Sq   F value Pr(>F)    
## 1  13136      38463                                
## 2  13135      38460  1    2.41    0.8233 0.3642    
## 3  13134      35348  1 3112.72 1156.5800 <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 70023.05
## 2     2 70024.23
## 3     3 68917.18

## 
## Formula: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * 
##     (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * 
##     exp(-((log(STDAGE_t1/c))/d)^2))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge    -0.433522   0.115029  -3.769 0.000165 ***
## phi   -0.010223   0.005051  -2.024 0.042995 *  
## alpha  0.872259   0.022753  38.337  < 2e-16 ***
## a      4.054684   0.137969  29.388  < 2e-16 ***
## b      3.131202   0.136903  22.872  < 2e-16 ***
## c     16.381538   0.414907  39.482  < 2e-16 ***
## d      0.881226   0.048681  18.102  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.641 on 13134 degrees of freedom
## 
## Number of iterations to convergence: 6 
## Achieved convergence tolerance: 6.873e-06
##   (71 observations deleted due to missingness)

summary

simple model: fits
phi model: fits
phi-alpha model: fits

plot residuals

predict and plot

## Warning: Removed 493 rows containing non-finite values (stat_summary_bin).

## Warning: Removed 532 rows containing missing values (geom_point).

## Warning: Removed 1 rows containing missing values (geom_pointrange).

## Warning: Removed 82 row(s) containing missing values (geom_path).

plotting 2

234 - Lower Mississippi Riverine Forest

model selection 1

## Error in nls(fg2_1, data = G_234, start = c(ge = ge.start, a = a.start,  : 
##   singular gradient
## Analysis of Variance Table
## 
## Model 1: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 2: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   1320     4762.7                                
## 2   1319     4576.0  1 186.65  53.798 3.865e-13 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1       NA
## 2     2 7288.969
## 3     3 7237.959

## 
## Formula: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * 
##     (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * 
##     exp(-((log(STDAGE_t1/c))/d)^2))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge     1.331021   1.277561   1.042  0.29767    
## phi    0.008008   0.026481   0.302  0.76239    
## alpha  0.826641   0.101378   8.154 8.11e-16 ***
## a      3.056931   0.693416   4.409 1.13e-05 ***
## b      1.576055   0.494782   3.185  0.00148 ** 
## c     18.938597   3.082749   6.143 1.07e-09 ***
## d      0.808868   0.291207   2.778  0.00555 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.863 on 1319 degrees of freedom
## 
## Number of iterations to convergence: 33 
## Achieved convergence tolerance: 8.167e-06
##   (6 observations deleted due to missingness)

summary

simple model: does not fit
phi model: fits
phi-alpha model: fits ## plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.85296, p-value < 2.2e-16
## 
## 
## ------

## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -4.3992, p-value = 1.087e-05
## alternative hypothesis: two.sided

predict and plot

## Warning: Removed 46 rows containing non-finite values (stat_summary_bin).

## Warning: Removed 50 rows containing missing values (geom_point).

## Warning: Removed 1 rows containing missing values (geom_pointrange).

## Warning: Removed 61 row(s) containing missing values (geom_path).

plotting 2

242 - Pacific Lowland Mixed Forest

model selection 1

## Error in nls(fg2_1, data = G_242, start = c(ge = ge.start, a = a.start,  : 
##   singular gradient
## Analysis of Variance Table
## 
## Model 1: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 2: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
##   Res.Df Res.Sum Sq Df Sum Sq F value   Pr(>F)   
## 1     78     85.971                              
## 2     76     72.790  2  13.18  6.8807 0.001793 **
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1       NA
## 2     2 395.8674
## 3     3 380.5042

## 
## Formula: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * 
##     (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * 
##     exp(-((log(STDAGE_t1/c))/d)^2))
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## ge     0.21893    2.53852   0.086  0.93150    
## phi    0.03892    0.05628   0.692  0.49134    
## alpha  0.90881    0.29409   3.090  0.00279 ** 
## a      6.02581    3.06663   1.965  0.05307 .  
## b     -4.25479    2.51536  -1.692  0.09483 .  
## c     38.76418    1.45405  26.660  < 2e-16 ***
## d      0.11831    0.05408   2.188  0.03176 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.9787 on 76 degrees of freedom
## 
## Number of iterations to convergence: 25 
## Achieved convergence tolerance: 8.7e-06
##   (4 observations deleted due to missingness)

summary

simple model: does not fit
phi model: fits
phi-alpha model: fits

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.98592, p-value = 0.5037
## 
## 
## ------

## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = 1.4496, p-value = 0.1472
## alternative hypothesis: two.sided

predict and plot

## Warning: Removed 1 rows containing missing values (geom_point).

plotting 2

251 - Prairie Parkland (Temperate)

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 2: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 3: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
##   Res.Df Res.Sum Sq Df  Sum Sq F value    Pr(>F)    
## 1   1805     1761.3                                 
## 2   1804     1759.4  1  1.9299  1.9789    0.1597    
## 3   1803     1741.8  1 17.6581 18.2789 2.008e-05 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 6948.424
## 2     2 6948.440
## 3     3 6932.183

## 
## Formula: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * 
##     (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * 
##     exp(-((log(STDAGE_t1/c))/d)^2))
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## ge    -0.27353    0.33952  -0.806    0.421    
## phi    0.01316    0.01092   1.205    0.228    
## alpha  0.42364    0.09491   4.464 8.56e-06 ***
## a     -0.52751    6.93253  -0.076    0.939    
## b      3.74176    6.93382   0.540    0.590    
## c     26.97146    5.94271   4.539 6.04e-06 ***
## d      3.61151    4.02790   0.897    0.370    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.9829 on 1803 degrees of freedom
## 
## Number of iterations to convergence: 10 
## Achieved convergence tolerance: 6.948e-06
##   (9 observations deleted due to missingness)

summary

simple model: fits
phi model: fits
phi-alpha model: fits

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.91385, p-value < 2.2e-16
## 
## 
## ------

## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -9.8187, p-value < 2.2e-16
## alternative hypothesis: two.sided

predict and plot

## Warning: Removed 7 rows containing missing values (geom_point).

plotting 2

255 - Prairie Parkland (Subtropical)

model selection 1

## Warning in log(STDAGE_t1/c): NaNs produced

## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model

## Warning in log(STDAGE_t1/c): NaNs produced

## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model

## Warning in log(STDAGE_t1/c): NaNs produced

## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
##   model AIC
## 1     1  NA
## 2     2  NA
## 3     3  NA

## Warning in min(AIC1_255$AIC, na.rm = T): no non-missing arguments to min;
## returning Inf

## Error in h(simpleError(msg, call)) : 
##   error in evaluating the argument 'object' in selecting a method for function 'summary': object 'nls_255.' not found

summary

simple model: does not fit
phi model: does not fit
phi-alpha model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

261 - California Coastal Chaparral Forest and Shrub

model selection 1

summary

simple model: does not fit
phi model: does not fit
phi-alpha model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

262 - California Dry Steppe

model selection 1

summary

simple model: does not fit
phi model: does not fit
phi-alpha model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

263 - California Coastal Steppe - Mixed Forest and Redwood Forest

model selection 1

## Warning in log(STDAGE_t1/c): NaNs produced

## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model

## Warning in log(STDAGE_t1/c): NaNs produced

## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model

## Warning in log(STDAGE_t1/c): NaNs produced

## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
##   model AIC
## 1     1  NA
## 2     2  NA
## 3     3  NA

## Warning in min(AIC1_263$AIC, na.rm = T): no non-missing arguments to min;
## returning Inf

## Error in h(simpleError(msg, call)) : 
##   error in evaluating the argument 'object' in selecting a method for function 'summary': object 'nls_263.' not found

summary

simple model: does not fit
phi model: does not fit
phi-alpha model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

313 - Colorado Plateau Semi-Desert

model selection 1

## Warning in log(STDAGE_t1/c): NaNs produced

## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model

## Warning in log(STDAGE_t1/c): NaNs produced

## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model

## Warning in log(STDAGE_t1/c): NaNs produced

## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
##   model AIC
## 1     1  NA
## 2     2  NA
## 3     3  NA

## Warning in min(AIC1_313$AIC, na.rm = T): no non-missing arguments to min;
## returning Inf

## Error in h(simpleError(msg, call)) : 
##   error in evaluating the argument 'object' in selecting a method for function 'summary': object 'nls_313.' not found

summary

simple model: does not fit
phi model: does not fit
phi-alpha model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

315 - Southwest Plateau and Plains Dry Steppe and Shrub

model selection 1

## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
##   model AIC
## 1     1  NA
## 2     2  NA
## 3     3  NA
## Error in h(simpleError(msg, call)) : 
##   error in evaluating the argument 'object' in selecting a method for function 'summary': object 'nls_315.' not found

summary

simple model: does not fit
phi model: does not fit
phi-alpha model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

321 - Chihuahuan Semi-Desert

model selection 1

summary

simple model: does not fit
phi model: does not fit
phi-alpha model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

322 - American Semidesert and Desert

model selection 1

## Error in nls(fg2_1, data = G_322, start = c(ge = ge.start, a = a.start,  : 
##   missing or negative weights not allowed
## Error in nls(fg2_2, data = G_322, start = c(ge = ge.start, phi = phi.start,  : 
##   missing or negative weights not allowed
## Error in nls(fg2_3, data = G_322, start = c(ge = ge.start, phi = phi.start,  : 
##   missing or negative weights not allowed
##   model AIC
## 1     1  NA
## 2     2  NA
## 3     3  NA

## Warning in min(AIC1_322$AIC, na.rm = T): no non-missing arguments to min;
## returning Inf

## Error in h(simpleError(msg, call)) : 
##   error in evaluating the argument 'object' in selecting a method for function 'summary': object 'nls_322.' not found

summary

simple model: does not fit
phi model: does not fit
phi-alpha model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

331 - Great Plains/Palouse Dry Steppe

model selection 1

summary

simple model: does not fit
phi model: does not fit
phi-alpha model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

332 - Great Plains Steppe

model selection 1

summary

simple model: does not fit
phi model: does not fit
phi-alpha model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

341 - Intermountain Semi-desert & Desert

model selection 1

summary

simple model: does not fit
phi model: does not fit
phi-alpha model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

342 - Intermountain Semi-Desert

model selection 1

## Warning in log(STDAGE_t1/c): NaNs produced

## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model

## Warning in log(STDAGE_t1/c): NaNs produced

## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model

## Warning in log(STDAGE_t1/c): NaNs produced

## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
##   model AIC
## 1     1  NA
## 2     2  NA
## 3     3  NA
## Error in h(simpleError(msg, call)) : 
##   error in evaluating the argument 'object' in selecting a method for function 'summary': object 'nls_342.' not found

summary

simple model: does not fit
phi model: does not fit
phi-alpha model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

411 - Everglades

model selection 1

summary

simple model: does not fit
phi model: does not fit
phi-alpha model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

M211 - Adirondack-New England Mixed forest - Coniferous Forest - Alpine Meadow

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 2: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 3: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   6739     4646.2                                
## 2   6738     4626.6  1  19.59  28.533 9.515e-08 ***
## 3   6737     4305.1  1 321.53 503.155 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 24227.13
## 2     2 24200.63
## 3     3 23716.87

## 
## Formula: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * 
##     (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * 
##     exp(-((log(STDAGE_t1/c))/d)^2))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge     0.839453   0.191191   4.391 1.15e-05 ***
## phi    0.017716   0.004021   4.406 1.07e-05 ***
## alpha  0.637818   0.026454  24.111  < 2e-16 ***
## a      2.454269   0.124784  19.668  < 2e-16 ***
## b      0.706016   0.082147   8.595  < 2e-16 ***
## c     27.906459   1.761889  15.839  < 2e-16 ***
## d      0.939334   0.155412   6.044 1.58e-09 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.7994 on 6737 degrees of freedom
## 
## Number of iterations to convergence: 11 
## Achieved convergence tolerance: 4.749e-06
##   (2 observations deleted due to missingness)

summary

simple model: fits
phi model: fits
phi-alpha model: fits

plot residuals

predict and plot

## Warning: Removed 247 rows containing non-finite values (stat_summary_bin).

## Warning: Removed 249 rows containing missing values (geom_point).

## Warning: Removed 1 rows containing missing values (geom_pointrange).

## Warning: Removed 101 row(s) containing missing values (geom_path).

plotting 2

M221 - Eastern Broadleaf Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 2: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 3: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   8426      17788                                
## 2   8425      17756  1  31.86  15.118 0.0001018 ***
## 3   8424      17410  1 346.23 167.530 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 41529.83
## 2     2 41516.71
## 3     3 41352.69

## 
## Formula: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * 
##     (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * 
##     exp(-((log(STDAGE_t1/c))/d)^2))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge    -0.919201   0.118686  -7.745 1.07e-14 ***
## phi   -0.022794   0.006449  -3.535 0.000411 ***
## alpha  0.785104   0.057628  13.624  < 2e-16 ***
## a      3.546943   0.544737   6.511 7.88e-11 ***
## b      2.666305   0.482445   5.527 3.36e-08 ***
## c     22.383920   1.986010  11.271  < 2e-16 ***
## d      1.409723   0.295997   4.763 1.94e-06 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.438 on 8424 degrees of freedom
## 
## Number of iterations to convergence: 7 
## Achieved convergence tolerance: 2.011e-06
##   (1 observation deleted due to missingness)

summary

simple model: fits
phi model: fits
phi-alpha model: fits

plot residuals

predict and plot

## Warning: Removed 280 rows containing non-finite values (stat_summary_bin).

## Warning: Removed 280 rows containing missing values (geom_point).

## Warning: Removed 1 rows containing missing values (geom_pointrange).

## Warning: Removed 58 row(s) containing missing values (geom_path).

plotting 2

M223 - Ozark Broadleaf Forest Meadow

model selection 1

## Warning in log(STDAGE_t1/c): NaNs produced

## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
##   model      AIC
## 1     1 3577.901
## 2     2       NA
## 3     3 3546.760

## 
## Formula: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * 
##     (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * 
##     exp(-((log(STDAGE_t1/c))/d)^2))
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## ge     2.69640    1.44772   1.863   0.0629 .  
## phi   -0.03398    0.02232  -1.522   0.1283    
## alpha  0.88836    0.14021   6.336 3.76e-10 ***
## a      1.62042    0.32551   4.978 7.73e-07 ***
## b      1.18139    0.33243   3.554   0.0004 ***
## c     27.82096    2.51612  11.057  < 2e-16 ***
## d     -0.50622    0.11971  -4.229 2.59e-05 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.124 on 882 degrees of freedom
## 
## Number of iterations to convergence: 33 
## Achieved convergence tolerance: 8.237e-06
##   (1 observation deleted due to missingness)

summary

simple model: fits
phi model: does not fit
phi-alpha model: fits

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.97086, p-value = 2.421e-12
## 
## 
## ------

## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -2.2847, p-value = 0.02233
## alternative hypothesis: two.sided

predict and plot

## Warning: Removed 23 rows containing non-finite values (stat_summary_bin).

## Warning: Removed 23 rows containing missing values (geom_point).

## Warning: Removed 1 rows containing missing values (geom_pointrange).

## Warning: Removed 21 row(s) containing missing values (geom_path).

plotting 2

M231 - Ouachita Mixed Forest

model selection 1

## Error in nls(fg2_1, data = G_M231, start = c(ge = ge.start, a = a.start,  : 
##   number of iterations exceeded maximum of 50

## Warning in log(STDAGE_t1/c): NaNs produced

## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model

## Warning in log(STDAGE_t1/c): NaNs produced

## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
##   model AIC
## 1     1  NA
## 2     2  NA
## 3     3  NA

## Warning in min(AIC1_M231$AIC, na.rm = T): no non-missing arguments to min;
## returning Inf

## Error in h(simpleError(msg, call)) : 
##   error in evaluating the argument 'object' in selecting a method for function 'summary': object 'nls_M231.' not found

summary

simple model: does not fit
phi model: does not fit
phi-alpha model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

M242 - Cascade Mixed Forest

model selection 1

## Warning in log(STDAGE_t1/c): NaNs produced

## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
## Analysis of Variance Table
## 
## Model 1: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 2: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   3322     9820.3                                
## 2   3317     9330.6  5 489.69  34.817 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1       NA
## 2     2 17465.07
## 3     3 17280.16

## 
## Formula: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * 
##     (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * 
##     exp(-((log(STDAGE_t1/c))/d)^2))
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## ge    -1.56077    0.27311  -5.715 1.20e-08 ***
## phi   -0.01051    0.01704  -0.617    0.537    
## alpha  1.04948    0.07321  14.335  < 2e-16 ***
## a      5.92520    0.51987  11.398  < 2e-16 ***
## b      4.73611    0.67704   6.995 3.19e-12 ***
## c     33.08842    1.19266  27.743  < 2e-16 ***
## d      0.39861    0.04588   8.688  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.677 on 3317 degrees of freedom
## 
## Number of iterations to convergence: 12 
## Achieved convergence tolerance: 6.321e-06
##   (80 observations deleted due to missingness)

summary

simple model: does not fit
phi model: fits
phi-alpha model: fits

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.88609, p-value < 2.2e-16
## 
## 
## ------

## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -13.849, p-value < 2.2e-16
## alternative hypothesis: two.sided

predict and plot

## Warning: Removed 144 rows containing non-finite values (stat_summary_bin).

## Warning: Removed 160 rows containing missing values (geom_point).

## Warning: Removed 1 rows containing missing values (geom_pointrange).

## Warning: Removed 543 row(s) containing missing values (geom_path).

plotting 2

M261 - Sierran Steppe - Mixed Forest - Coniferous Forest - Alpine Meadow

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 2: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 3: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
##   Res.Df Res.Sum Sq Df Sum Sq  F value    Pr(>F)    
## 1   1993     4061.0                                 
## 2   1992     3841.0  1 219.95 114.0694 < 2.2e-16 ***
## 3   1983     3700.5  9 140.49   8.3651 2.464e-12 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 9377.060
## 2     2 9267.803
## 3     3 9164.998

## 
## Formula: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * 
##     (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * 
##     exp(-((log(STDAGE_t1/c))/d)^2))
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## ge    -1.57872    0.29513  -5.349 9.85e-08 ***
## phi    0.18599    0.01376  13.516  < 2e-16 ***
## alpha  0.79954    0.08748   9.140  < 2e-16 ***
## a      3.80300    1.12004   3.395 0.000699 ***
## b      4.30989    1.10875   3.887 0.000105 ***
## c     33.42758    7.29476   4.582 4.88e-06 ***
## d      1.75074    0.51733   3.384 0.000728 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.366 on 1983 degrees of freedom
## 
## Number of iterations to convergence: 18 
## Achieved convergence tolerance: 7.259e-06
##   (40 observations deleted due to missingness)

summary

simple model: fits
phi model: fits
phi-alpha model: fits

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.94641, p-value < 2.2e-16
## 
## 
## ------

## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -2.0268, p-value = 0.04268
## alternative hypothesis: two.sided

predict and plot

## Warning: Removed 6 rows containing missing values (geom_point).

plotting 2

M262 - Califormia Coastal Range = Coniferous Forest - Open woodland Shrub Meadow

model selection 1

summary

simple model: does not fit
phi model: does not fit
phi-alpha model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

M313 - Arizona-New Mexico Mountains Semi-Desert - Open Woodland - Coniferous Forest - Alpine Meadow

model selection 1

## Warning in log(STDAGE_t1/c): NaNs produced

## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model

## Warning in log(STDAGE_t1/c): NaNs produced

## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model

## Warning in log(STDAGE_t1/c): NaNs produced

## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
##   model AIC
## 1     1  NA
## 2     2  NA
## 3     3  NA

## Warning in min(AIC1_M313$AIC, na.rm = T): no non-missing arguments to min;
## returning Inf

## Error in h(simpleError(msg, call)) : 
##   error in evaluating the argument 'object' in selecting a method for function 'summary': object 'nls_M313.' not found

summary

simple model: does not fit
phi model: does not fit
phi-alpha model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

M331 - Southern Rocky Mountain Steppe - Open Woodland - Coniferous Forest - Alpine Meadow

model selection 1

## Warning in log(STDAGE_t1/c): NaNs produced

## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model

## Warning in log(STDAGE_t1/c): NaNs produced

## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model

## Warning in log(STDAGE_t1/c): NaNs produced

## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
##   model AIC
## 1     1  NA
## 2     2  NA
## 3     3  NA

## Warning in min(AIC1_M331$AIC, na.rm = T): no non-missing arguments to min;
## returning Inf

## Error in h(simpleError(msg, call)) : 
##   error in evaluating the argument 'object' in selecting a method for function 'summary': object 'nls_M331.' not found

summary

simple model: does not fit
phi model: does not fit
phi-alpha model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

M332 - Middle Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 2: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 3: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
##   Res.Df Res.Sum Sq Df Sum Sq F value  Pr(>F)    
## 1   2621     2927.8                              
## 2   2620     2921.0  1   6.83  6.1259 0.01338 *  
## 3   2610     2716.8 10 204.15 19.6125 < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 9126.760
## 2     2 9122.627
## 3     3 8914.997

## 
## Formula: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * 
##     (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * 
##     exp(-((log(STDAGE_t1/c))/d)^2))
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## ge    -0.77373    0.44346  -1.745  0.08114 .  
## phi    0.03730    0.01613   2.313  0.02080 *  
## alpha  0.84336    0.05298  15.918  < 2e-16 ***
## a      0.54605    1.16983   0.467  0.64070    
## b      2.23565    1.19591   1.869  0.06168 .  
## c     56.99643    4.61322  12.355  < 2e-16 ***
## d      2.14750    0.78713   2.728  0.00641 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.02 on 2610 degrees of freedom
## 
## Number of iterations to convergence: 10 
## Achieved convergence tolerance: 5.3e-06
##   (64 observations deleted due to missingness)

summary

simple model: fits
phi model: fits
phi-alpha model: fits

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.87747, p-value < 2.2e-16
## 
## 
## ------

## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -6.8087, p-value = 9.852e-12
## alternative hypothesis: two.sided

predict and plot

## Warning: Removed 107 rows containing non-finite values (stat_summary_bin).

## Warning: Removed 119 rows containing missing values (geom_point).

## Warning: Removed 1 rows containing missing values (geom_pointrange).

## Warning: Removed 193 row(s) containing missing values (geom_path).

plotting 2

M333 - Northern Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow

model selection 1

## Error in nls(fg2_1, data = G_M333, start = c(ge = ge.start, a = a.start,  : 
##   singular gradient

## Warning in log(STDAGE_t1/c): NaNs produced

## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model

## Warning in log(STDAGE_t1/c): NaNs produced

## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
##   model AIC
## 1     1  NA
## 2     2  NA
## 3     3  NA

## Warning in min(AIC1_M333$AIC, na.rm = T): no non-missing arguments to min;
## returning Inf

## Error in h(simpleError(msg, call)) : 
##   error in evaluating the argument 'object' in selecting a method for function 'summary': object 'nls_M333.' not found

summary

simple model: does not fit
phi model: does not fit
phi-alpha model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

M334 - Black Hills Coniferous Forest

model selection 1

## Warning in log(STDAGE_t1/c): NaNs produced

## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
## Error in nls(fg2_2, data = G_M334, start = c(ge = ge.start, phi = phi.start,  : 
##   singular gradient
## Error in nls(fg2_3, data = G_M334, start = c(ge = ge.start, phi = phi.start,  : 
##   number of iterations exceeded maximum of 50
##   model AIC
## 1     1  NA
## 2     2  NA
## 3     3  NA

## Warning in min(AIC1_M334$AIC, na.rm = T): no non-missing arguments to min;
## returning Inf

## Error in h(simpleError(msg, call)) : 
##   error in evaluating the argument 'object' in selecting a method for function 'summary': object 'nls_M334.' not found

summary

simple model: does not fit
phi model: does not fit
phi-alpha model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

M341 - Nevada-Utah Mountains Semi-Desert - Coniferous Forest - Alpine Meadow

model selection 1

summary

simple model: does not fit
phi model: does not fit
phi-alpha model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

Fitted parameters

Best / selected models by ecoprovince

Code	Ecoregion	Sel.Mod
211	Northeastern Mixed Forest	3
212	Laurentian Mixed Forest	3
221	Eastern Broadleaf Forest	2
222	Midwest Broadleaf Forest	NA
223	Central Interior Broadleaf Forest	3
231	Southeastern Mixed Forest	3
232	Outer Coastal Plain Mixed Forest	3
234	Lower Mississippi Riverine Forest	3
242	Pacific Lowland Mixed Forest	3
251	Prairie Parkland (Temperate)	3
255	Prairie Parkland (Subtropical)	NA
261	California Coastal Chaparral Forest and Shrub	NA
262	California Dry Steppe	NA
263	California Coastal Steppe - Mixed Forest and Redwood Forest	NA
313	Colorado Plateau Semi-Desert	NA
315	Southwest Plateau and Plains Dry Steppe and Shrub	NA
321	Chihuahuan Semi-Desert	NA
322	American Semidesert and Desert	NA
331	Great Plains/Palouse Dry Steppe	NA
332	Great Plains Steppe	NA
341	Intermountain Semi-Desert and Desert	NA
342	Intermountain Semi-Desert	NA
411	Everglades	NA
M211	Adirondack-New England Mixed forest - Coniferous Forest - Alpine Meadow	3
M221	Central Appalachian Broadleaf Forest - Coniferous Forest - Meadow	3
M223	Ozark Broadleaf Forest Meadow	3
M231	Ouachita Mixed Forest	NA
M242	Cascade Mixed Forest	3
M261	Sierran Steppe - Mixed Forest - Coniferous Forest - Alpine Meadow	3
M262	California Coastal Range Coniferous Forest - Open Woodland - Shrub - Meadow	NA
M313	Arizona-New Mexico Mountains Semi-Desert - Open Woodland - Coniferous Forest - Alpine Meadow	NA
M331	Southern Rocky Mountain Steppe - Open Woodland - Coniferous Forest - Alpine Meadow	NA
M332	Middle Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow	3
M333	Northern Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow	NA
M334	Black Hills Coniferous Forest	NA
M341	Nevada-Utah Mountains Semi-Desert - Coniferous Forest - Alpine Meadow	NA

table by ecoprovince

Code	Ecoregion	region	n.obs	n.plots	ge	ge.2.5	ge.97.5	phi	phi.2.5	phi.97.5	alpha	alpha.2.5	alpha.97.5	a	a.2.5	a.97.5	b	b.2.5	b.97.5	c	c.2.5	c.97.5	d	d.2.5	d.97.5
211	Northeastern Mixed Forest	east	6825	2859	0.2874589	-0.0322888	0.6072066	0.0104502	0.0019270	0.0189735	0.6429503	0.5840195	0.7018810	-6.7088010	-41.2838864	27.866284	10.1220869	-24.4326577	44.6768315	29.51577	25.66346	33.36808	5.0235276	-4.2039126	14.2509677
212	Laurentian Mixed Forest	east	18886	8936	0.8051263	0.5296386	1.0806140	0.0265601	0.0207928	0.0323274	0.8265606	0.7853994	0.8677219	1.1846067	0.7987248	1.570489	1.4378769	1.0727087	1.8030450	19.81273	18.27704	21.34842	1.8969248	1.4778470	2.3160026
221	Eastern Broadleaf Forest	east	7329	3559	-1.3457005	-1.5313516	-1.1600494	0.0026268	-0.0069870	0.0122406	NA	NA	NA	4.8785600	4.6447631	5.112357	0.7610893	0.1154287	1.4067499	25.24486	22.40844	28.08128	-0.1441024	-0.2831518	-0.0050530
222	Midwest Broadleaf Forest	east	4923	2431	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA
223	Central Interior Broadleaf Forest	east	8914	3781	-1.3095074	-1.4948708	-1.1241440	-0.0244119	-0.0358968	-0.0129271	0.6036573	0.5248380	0.6824765	2.6051538	1.2437763	3.966531	2.3138939	0.9775443	3.6502435	27.31140	23.43780	31.18501	1.6205945	0.8767802	2.3644088
231	Southeastern Mixed Forest	east	13401	6113	-0.6976600	-0.8796939	-0.5156262	-0.0163198	-0.0257474	-0.0068922	0.8940459	0.8489688	0.9391230	3.9091946	3.3985539	4.419835	4.0826651	3.6100997	4.5552306	18.00850	17.14590	18.87110	1.2376798	1.0745533	1.4008063
232	Outer Coastal Plain Mixed Forest	east	13212	6392	-0.4335225	-0.6589964	-0.2080486	-0.0102231	-0.0201239	-0.0003223	0.8722590	0.8276606	0.9168573	4.0546841	3.7842445	4.325124	3.1312016	2.8628523	3.3995509	16.38154	15.56826	17.19482	0.8812257	0.7858048	0.9766467
234	Lower Mississippi Riverine Forest	east	1332	744	1.3310210	-1.1752514	3.8372934	0.0080081	-0.0439415	0.0599576	0.8266407	0.6277610	1.0255203	3.0569307	1.6966130	4.417248	1.5760551	0.6054087	2.5467015	18.93860	12.89097	24.98622	0.8088683	0.2375887	1.3801478
242	Pacific Lowland Mixed Forest	pacific	87	87	0.2189324	-4.8369759	5.2748406	0.0389228	-0.0731777	0.1510232	0.9088109	0.3230842	1.4945376	6.0258092	-0.0819196	12.133538	-4.2547925	-9.2645580	0.7549730	38.76418	35.86820	41.66017	0.1183081	0.0106045	0.2260116
251	Prairie Parkland (Temperate)	east	1819	819	-0.2735319	-0.9394195	0.3923556	0.0131621	-0.0082566	0.0345808	0.4236413	0.2374933	0.6097892	-0.5275078	-14.1241533	13.069138	3.7417555	-9.8574119	17.3409230	26.97146	15.31613	38.62679	3.6115127	-4.2883307	11.5113561
255	Prairie Parkland (Subtropical)	pacific	674	298	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA
261	California Coastal Chaparral Forest and Shrub	pacific	27	27	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA
262	California Dry Steppe	pacific	0	0	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA
263	California Coastal Steppe - Mixed Forest and Redwood Forest	pacific	173	173	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA
313	Colorado Plateau Semi-Desert	interior west	215	215	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA
315	Southwest Plateau and Plains Dry Steppe and Shrub	interior west	4	4	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA
321	Chihuahuan Semi-Desert	interior west	9	9	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA
322	American Semidesert and Desert	interior west	3	3	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA
331	Great Plains/Palouse Dry Steppe	interior west	310	242	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA
332	Great Plains Steppe	interior west	195	106	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA
341	Intermountain Semi-Desert and Desert	interior west	62	62	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA
342	Intermountain Semi-Desert	interior west	121	120	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA
411	Everglades	east	93	61	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA
M211	Adirondack-New England Mixed forest - Coniferous Forest - Alpine Meadow	east	6746	2998	0.8394531	0.4646580	1.2142481	0.0177158	0.0098341	0.0255975	0.6378178	0.5859605	0.6896751	2.4542693	2.2096525	2.698886	0.7060158	0.5449813	0.8670504	27.90646	24.45260	31.36032	0.9393341	0.6346776	1.2439905
M221	Central Appalachian Broadleaf Forest - Coniferous Forest - Meadow	east	8432	3849	-0.9192014	-1.1518555	-0.6865474	-0.0227936	-0.0354347	-0.0101524	0.7851036	0.6721383	0.8980689	3.5469427	2.4791244	4.614761	2.6663048	1.7205935	3.6120162	22.38392	18.49085	26.27699	1.4097232	0.8294956	1.9899507
M223	Ozark Broadleaf Forest Meadow	east	890	346	2.6963990	-0.1449729	5.5377709	-0.0339763	-0.0777800	0.0098274	0.8883603	0.6131784	1.1635421	1.6204165	0.9815431	2.259290	1.1813938	0.5289410	1.8338467	27.82096	22.88268	32.75923	-0.5062169	-0.7411607	-0.2712730
M231	Ouachita Mixed Forest	east	988	481	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA
M242	Cascade Mixed Forest	pacific	3404	3384	-1.5607736	-2.0962569	-1.0252903	-0.0105068	-0.0439108	0.0228972	1.0494784	0.9059351	1.1930217	5.9252007	4.9059108	6.944491	4.7361090	3.4086420	6.0635761	33.08842	30.75000	35.42683	0.3986055	0.3086487	0.4885623
M261	Sierran Steppe - Mixed Forest - Coniferous Forest - Alpine Meadow	pacific	2030	2024	-1.5787192	-2.1575161	-0.9999223	0.1859908	0.1590037	0.2129779	0.7995398	0.6279842	0.9710954	3.8030004	1.6064142	5.999587	4.3098883	2.1354531	6.4843235	33.42758	19.12137	47.73378	1.7507415	0.7361737	2.7653093
M262	California Coastal Range Coniferous Forest - Open Woodland - Shrub - Meadow	interior west	19	19	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA
M313	Arizona-New Mexico Mountains Semi-Desert - Open Woodland - Coniferous Forest - Alpine Meadow	interior west	362	362	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA
M331	Southern Rocky Mountain Steppe - Open Woodland - Coniferous Forest - Alpine Meadow	interior west	1713	1713	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA
M332	Middle Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow	interior west	2681	2671	-0.7737332	-1.6433049	0.0958386	0.0372978	0.0056780	0.0689176	0.8433571	0.7394668	0.9472473	0.5460495	-1.7478438	2.839943	2.2356502	-0.1093856	4.5806859	56.99643	47.95049	66.04237	2.1474997	0.6040457	3.6909537
M333	Northern Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow	interior west	1678	1678	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA
M334	Black Hills Coniferous Forest	interior west	365	171	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA
M341	Nevada-Utah Mountains Semi-Desert - Coniferous Forest - Alpine Meadow	interior west	213	213	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA

plot ge

map

## OGR data source with driver: ESRI Shapefile 
## Source: "C:\Users\hogan.jaaron\Dropbox\FIA_R\Mapping\S_USA.EcoMapProvinces\S_USA.EcoMapProvinces.shp", layer: "S_USA.EcoMapProvinces"
## with 37 features
## It has 17 fields
## Integer64 fields read as strings:  PROVINCE_ PROVINCE_I

map2

## Warning: package 'ggnewscale' was built under R version 4.2.1

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family not found in Windows font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family not found in Windows font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family not found in Windows font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family not found in Windows font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family not found in Windows font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family not found in Windows font database

plot phi (effect of DeltaPDSI)

plot alpha (biomass growth compensation effect)

plot a coefficient

## Warning: Removed 21 rows containing missing values (geom_point).

plot b coefficient

## Warning: Removed 21 rows containing missing values (geom_point).

plot c coefficient

## Warning: Removed 1 rows containing missing values (geom_hline).

## Warning: Removed 21 rows containing missing values (geom_point).

plot d coefficient

## Warning: Removed 22 rows containing missing values (geom_point).

Caclulations - weighted averages

ge (stand biomass growth enhancement factor in % 2000-2021)

##          region weighted.ge
## 1     entire US  -0.3267201
## 2       pacific  -1.4113029
## 3          east  -0.1863573
## 4 interior west  -0.2723565

phi (effect of DeltaPDSI)

##          region  weighted.phi
## 1     entire US  0.0076104930
## 2       pacific  0.0574464617
## 3          east -0.0002416832
## 4 interior west  0.0131289526

alpha (biomass growth compensation effect)

##          region weighted.alpha
## 1     entire US      0.6365641
## 2       pacific      0.8758168
## 3          east      0.6629378
## 4 interior west      0.2968644

FIA - NLS Models: Biomass Growth vs. Stand Age

JAH

2022-10-17

Background

211 - Northeastern Mixed Forest

model selection 1

summary

plot residuals

predict and plot

plotting 2

212 - Laurentian Mixed Forest

model selection 1

summary

plot residuals

predict and plot

plotting 2

221 - Eastern Broadleaf Forest

model selection 1

summary

plot residuals

predict and plot

plotting 2

222 - Midwest Broadleaf Forest

model selection 1

summary

plot residuals

predict and plot

plotting 2

223 - Central Interior Broadleaf Forest

model selection 1

summary

plot residuals

predict and plot

plotting 2

231 - Southeastern Mixed Forest

model selection 1

summary

plot residuals

predict and plot

plotting 2

232 - Outer Coastal Plain Mixed Forest

model selection 1

summary

plot residuals

predict and plot

plotting 2

234 - Lower Mississippi Riverine Forest

model selection 1

summary

predict and plot

plotting 2

242 - Pacific Lowland Mixed Forest

model selection 1

summary

plot residuals

predict and plot

plotting 2

251 - Prairie Parkland (Temperate)

model selection 1

summary

plot residuals

predict and plot

plotting 2

255 - Prairie Parkland (Subtropical)

model selection 1

summary

plot residuals

predict and plot

plotting 2

261 - California Coastal Chaparral Forest and Shrub

model selection 1

summary

plot residuals

predict and plot

plotting 2

262 - California Dry Steppe

model selection 1

summary

plot residuals

predict and plot